A recent development in television is the use of high Q series resonant circuit for developing voltages of the order of 70

kV for high intensity, projection-type tubes.

Most resonant radio frequency circuits are made with a variable element so that the frequency of resonance may be

adjusted. A radio receiver, for example, contains several adjustable resonant circuits. Probably the most common

means of adjustment is the variable capacitor. Since the development of the powdered iron core, variation of

inductance has also become simple and popular. At high frequencies, such coils are sometimes resonated with their

distributed capacitance and that of the associated wiring. Using the equation for the frequency of resonance,

you can see that decreasing L, C, or both, results in an increased resonant frequency.

The simplest parallel resonant circuit is inductance and capacitance in parallel, connected to a generator as shown in

figure 1-7. For simplicity, assume that there is no resistance in L or C. The frequency is such that XL = XC. The

currents through the two branches are then equal.

IL = IC, or IL - IC = 0

or vectorially,

jIL - jIC = 0.

Adding these currents to find the total current shows their vector sum to be zero. Since no current is drawn from the

generator, this theoretically perfect resonant circuit has infinite impedance. This is directly opposite to the condition of

series resonance. The requirement that XL = XC is, of course, the same as that of the series resonant circuit. Because

of this, the equation for frequency of resonance,

is the same for both series and parallel circuits.